J . Phys. Chem. 1990, 94, 1326-1329
7326
Molecular Motion in Sucrose-Water Mixtures in the Liquid and Glassy State As Studied by Spln Probe ESR M. J. C. W. Roozenf and M. A. Hemminga*,t Laboratory of Dairying and Food Physics, Department of Food Science, and Department of Molecular Physics, Wageningen Agricultural University, 6700 E T Wageningen, The Netherlands (Received: February 23, 1990)
Conventional and saturation transfer ESR spectroscopies are used to study the rotational behavior of two different nitroxide spin probes-4-hydroxy-2,2,6,6-tetramethylpiperidinyloxy (Tempol) and 3-maleimido-2,2,5,5-tetramethyl1-pyrrolcdinyloxy-in sucrose-water and glycerol-water mixtures as a function of temperature. The results are discussed in terms of slip and stickiness of the spin probes, which depend on the strength of the hydrogen bonds between the probe and the solvent. Except for the maleimido spin probe in anhydrous glycerol, which can form an extended solvation shell, the slip increases as the water content of the mixture decreases. This is explained by a decrease of hydrogen bonds between the probe and the solvent. In sucrose-water mixtures above 70 wt % sucrose and in sucrose-water mixtures in the glassy state the spin probes are presumably present in cavities. At the temperature at which the transition from glassy state to solution takes place, as measured with differential scanning calorimetry. an extreme increase in rotational mobility of the probes can be observed.
Introduction During the past years there has been an increasing interest in systems in the glassy state.I4 A glass is an amorphous solid, which exhibits a glass transition? In amorphous materials the molecules are forming a nonperiodic and nonsymmetric network.I0 The glass transition is the phenomenon in which a solid amorphous phase exhibits a discontinuous change in the specific heat on changing the temperature. An essential prerequisite for glass formation from a solution is that the cooling rate must be sufficiently fast to preclude nucleation and crytal g r ~ w t h .At ~ the glass transition temperature, there is not only a sudden change in thermal and mechanical properties of the system but also an extreme decrease in the rates of molecular translation diffusion.” Due to very limited molecular motion, a food product in the glassy state is presumed not to decrease in quality during storage. The macroscopic properties of systems in the glassy state have been examined inten~ively,~”but only a limited amount of information is available about structural and dynamic properties at a molecular level. Simatos’*discussed the rotational mobility of spin probes in water-dextran mixtures. For water activities below 0.75 no probe mobility could be detected on a time scale of IO-’ s or less. Le Meste and DuckworthI3 studied the mobility of spin probes in concentrated caseinate solutions at room temperature. They observed an increase of rotational mobility above a water content of 0.25 g of water/(g of dry protein), which was ascribed to a glass-rubber transition. The present paper describes the application of conventional and saturation transfer electron spin resonance (ESR) spectroscopies to study the rotational mobility of spin probes in sucrose-water mixtures above and below the glass transition temperature. By use of conventional ESR as well as saturation transfer ESR, rotational mobilities between and IO-” s could be determined. As described by Jolicoeur14 and Le Meste and V ~ i l l e y , ’gly~ cerol-water mixtures were used as a reference system for this study. Theory To describe the isotropic rotational motion for small molecules in liquids, a modified Stokes-Einstein relationship has been proposedi6-I9
where 7, is the rotational correlation time, 7 the solvent viscosity, kb Boltzmann’s constant, V the volume of the rotating molecule, T the absolute temperature, T~ the zero-viscosity rotational cor-
* To whom
correspondence should be addressed.
’Laboratory of Dairying and Food Physics, Department of Food Science. f
Department of Molecular Physics.
TABLE I: van der Waals Volume V and Shape Parameter 0 for
Different Spin Probes probe
80
V,b A3
1 I1
0.05 0.10
310
Calculated according to
180
Hu and Z w a n ~ i g . *bCalculated ~ according
to B ~ n d i . * ~ relation time, and k a dimensionless interaction parameter. The meaning of T~ has been discussed previously, and often T~ has been assumed to be negligible.’9-21 The parameter k is a measure of the coupling of the rotational motions of the spin probe to the shear modes of the fluid. It has been found in many cases that 0 Ik I1 and that k is independent of temperature and viscosity. The parameter k depends, however, on specific solvent-probe interactions and on the geometry of the molecules considered, since nonspherical molecules must “displace” solvent as they rotate. This ( I ) Franks, F. In Properties of Water in Foods; Simatos, D., Multon, J., Eds.; Nijhoff Publishers: Dordrecht, 1985; pp 497-509. (2) Biliaderis, C. G.; Page, C. M.; Maurice, T. J.; Juliano, B. 0.J. Agric. Food Chem. 1986, 34, 16. (3) Levine, H.; Slade, L. In Food Structure: Its Creation and Evaluation; Blanshard, J. M. V., Mitchell, J. R., Eds.; Butterworths: London, 1988; pp 149-1 80. (4) Slade, L.; Levine, H. In Food Structure: Its Creation and Evaluation; Blanshard, J. M. V., Mitchell, J. R., Eds.; Butterworths: London, 1988; pp 115-148. (5) Simatos, D.; Karel, M. In Food Preservation by Moisture Control; Seow, C. C., Ed.; Elsevier Applied Science: Amsterdam, 1988; pp 1-41. (6) Simatos, D.; Blond, G.; Le Meste, M. Cryo-Lett. 1989, IO, 77. (7) Blond, G.Cryo-Lett. 1989, I O , 299. (8) Orford, P. D.; Parker, R.; Ring, S. G.; Smith, A. C. Int. J . Biol. Macromol. 1989, 1 I , 91. (9) Elliot, S. R. Physics of Amorphous Materials; Longman: London, 1983; Chapter I . (10) Flink, J. M. In Physical Properties ofFoods; Peleg, M., Bageley, E. B., Eds.; AVI Publishing Co. Inc.: Westport, CT, 1983; pp 473-521. (1 I ) Franks, F. Biophysics and Biochemistry at Low Temperatures; University Press: Cambridge, 1985; Chapter 3. (12) Simatos, D.; Le Meste, M.; Petroff, D.; Halphen, B. In Water Ac-
tivity: Influences on Food Quality; Rockland, L. B., Stewart, G. F., Eds.; Academic: Orlando, FL, 1981; pp 319-348. ( I 3) Le Meste, M.; Duckworth, R. B. Inr. J. Food. Sci. Technol. 1988, 23, 457. (14) Jolicoeur, C. J.; Friedman, H. L. Ber. Bunsen-Ges. Phys. Chem. 1971, 76, 248. (15) Le Meste, M.; Voilley, A. J. Phys. Chem. 1988, 92. 1612. (16) McClung, R. E. D.; Kivelson, D. J . Chem. Phys. 1968, 59, 3380-3391. (17) Kivelson, D.; Kivelson, M. G.;Oppenheim, I. J. Chem. Phys. 1970, 52, 1811. (18) Kowert, B.; Kivelson, D. J. Chem. Phys. 1976,64, 5206. (19) Dote, J. L.; Kivelson, D.; Schwartz, R. N. J . Phys. Chem. 1981,85, 2169. (20) Kivelson, D.; Madden, P. Annu. Rev. Phys. Chem. 1980, 31, 523. (21) Bauer, D. R.; Brauman, J. 1.; Pecora, R. J. Chem. Soc. 1973,6840.
0022-3654/90/2094-7326$02.50/00 1990 American Chemical Society
The Journal of Physical Chemistry. V O ~ 94, . NO. 18, 1990 7327
Molecular Motion in Sucrose Mixtures can be expressed as follows22 k = S(1 - e)
1
(2) in which S is the stickiness factor that depends on the coupling between the rotating molecule and the liquid. If S is zero, there is no interaction (complete slip conditions); for S equals one the boundary layer conditions are completely sticking. The parameter 6 is the ratio of the effectiveness of the torques under slip to those under stick conditions, and it depends on the geometry of the rotating molecule. Values derived from hydrodynamic theory have been tabulated for prolate and oblate spheroids as a function of the ratio of the short and long molecular axes.23 For the spin probes used in this study these values were determined by means of Stuart Briebleb atomic models. The values for parameter 6 are given in Table I . The volume Vis also given in this table; van der Waals incremental volumes as tabulated by B ~ n dwere i~~ used. For nonspherical molecules, S can be negative, implying that the molecules displace less solvent than is expected from their geometry. This is the case, for example, if a cavity is formed in which the probe can carry out "free rotation". k is then equal to zero, so that S equals -e( 1 - 8)-l (see eq 2). Materials and Methods Glycerol solutions were prepared by mixing 87% glycerol (Merck) and spin probe (Aldrich) solution. Concentrated glycerol solutions were prepared by drying the mixture at 102 OC. Anhydrous glycerol was obtained by drying during 60 h. Sucrose solutions were made by mixing sucrose (Merck) and spin probe solution during heating. The water content was determined from the refractive index as tabulated by WeasLzs The following nitroxide radicals were used:
OH
I
0'
I (Tempol)
.
+e
0
\/
.0 I1
The probe concentration in the samples was 0.2-0.5 mg/mL. ESR spectra were recorded on a Bruker ESR spectrometer 200D with nitrogen flow temperature control. For conventional ESR the microwave power was 1-5 mW. The scan range, scan rate, time constant, and modulation amplitude were adjusted so that distortion of the spectra was avoided. The rotational correlation time ( T ~ of ) weakly immobilized probes was estimated from the relation26 T~ = 6.5 x 1 0 - ~ ~ ~ { ( h , ,-/ h I)~ ) ~ ~ ~ where hHand hc are the heights of the high field and central lines, respectively. Bo is the line width of the central line in tesla. The rotational motion of the spin probes is assumed to be isotropic. In the slow motional region of the spin probes (7,between 10 and 200 ns), the rotational correlation time was obtained by using the method of G ~ l d m a n : ~ ~ T~ = a(1 - A',/A,)b A', is the separation of the outer hyperfine extrema in the ESR spectra, and A, is the rigid limiting value for the same quantity.
Both a and b depend on the nature of the motion of the probe and of the intrinsic line width of the spectra. For both sucrosewater mixtures and glycerol-water mixtures the Brownian dif(22) Hoel, D.; Kivelson, D. J . Chem. Phys. 1975, 62, 1323. (23) Hu. C. M.; Zwanzig, R . J . Chem. Phys. 1974, 60, 4345. (24) Bondi, A . J . Phys. Chem. 1964, 68, 441. (25) Weast, C. Handbook of Chemistry and Physics, 51st ed.; Chemical Rubber Co.: Boca Raton, FL, 1970. (26) Knowles, P. F.; Marsh, D.; Rattle, H. W. E. Magnetic Resonance of Biomolecules; Wiley: London, 1976. (27) Freed, J. H. In Spin Labeling, Theory and Applications; Berliner, L. J., Ed.; Academic Press: New York. 1976; pp 53-132.
0
20 40 60 BO 100 glycerol content I g glyceroV100 g mixture)
Figure 1. Parameter S a s a function of the glycerol content for glycerol-water mixtures: 0,spin probe I; 0 spin probe 11.
fusion model can be taken,28*29 resulting in a = 1.09 X 1 0-9 s and b = -1.05. Saturation transfer ESR is applied in the very slow motional region ( l O - ' s < T~ < s). Spectra were recorded under the following saturation conditions: microwave power 200 mW, a modulation amplitude of 1 mT. The ESR signal was recorded 90" out of phase with respect to the modulation signal. T~ was estimated by comparing the recorded spectra with standard spectra,Mrecorded in anhydrous glycerol under simular conditions as for the mixtures. Values of T~ between IO-' and lO-'s are accurate within a factor of 2.30 For sucrose-water mixtures that were studied at temperatures below the freezing point of water, the system was cooled rapidly to -70 "C and rewarmed to the temperature at which the spectrum was recorded. This ensures maximally frozen sample^.^' Results To analyze the interaction between the probe and the solvent in glycerol-water and sucrose-water mixtures at temperatures above the freezing point, graphs of the values for rc versus q / T were plotted (see eq 1 ; data not shown). Values for q for sucrose-water mixtures are obtained from Bates32and for glycerol-water mixtures from S e g ~ r .To ~ ~obtain values for k , from the slope of these graphs, the volume of the probe (see Table I) is considered to be independent of the composition of the solution. As shown in Table I, the van der Waals incremental volumes as tabulated by B ~ n d are i ~ used. ~ In the temperature range considered here, k was found to be independent of temperature. The ) between 1O-Io and s, in intercepts of these graphs ( T ~ are agreement with the results of other studies.I7 The parameter S describes specific solvent-probe interactions, which are independent of the shape of the probe. To obtain values for S from eq 2, values for 8 are used from Table I. To study variations of S with solvent composition, the value for 8 is considered to be independent of temperature and solvent effects. The same assumptions have been made for vanadyl acetylacetonate molecules in various alcohol systems.22 Figure 1 shows the parameter S as a function of the glycerol content in different glycerol-water mixtures. For both probes a decrease of S with increasing glycerol content can be observed up to a glycerol content of 95%. Above 95% an extreme increase in S of probe I1 is observed. This is not the case for probe I, which shows a continuous decrease up to 100%glycerol. The composition of the mixture at which for probe I1 a minimum in S can be (28) Le Meste, M.; Simatos, D. Cryo-Lett. 1980, I , 402. (29) Hyde, J . S. In Methods in Enzymology; Hirs, C . H. W., Timashef, S. N., Eds.; Academic Press: New York, 1978; pp 480-51 1 . (30) Hyde, J. S . In Molecular Motions in Polymers by ESR; Boyer, R. F., Keinath, S . E., Eds.; Harwords Academic Publisher: New York, 1978; pp 287-290. (31) Levine, H.; Slade, L. J . Chem. Soc.. Faraday. Trans. 1 1988, 84, 2619. (32) Bates, F. J. Polarimetry, Saccharimetry and the Sugars; Circ. C440; National Bureau of Standards: Washington, DC, 1942. (33) Segur. J. B.; Oberstar, H. Ind. Eng. Chem. 1951, 43, 21 17.
7328 The Journal of Physical Chemistry, Vol. 94, No. 18, 1990 1
j p = h
K
10-
\j
'-
70-*,
-70
r
!
,
-60
I
-50
!
-40
I
-30
1
I
-20
,
-10
r
10 T i"C1
0
Figure 3. rCas a function of temperature in a 20% sucrose-water mixture The temperature at which for spin probe I (0)and spin probe I1 (0). T~ starts to decrease sharply is indicated with an arrow (see text).
obtained is uncertain. This is due to experimental difficulties in estimating the water content in very concentrated glycerol water mixtures. In Figure 2 the parameter k is given as a function of the sucrose content in sucrose-water mixtures. A logarithmic plot of S (as in Figure I ) cannot be given here, since S becomes negative. The value of k at which this occurs is indicated with arrow 1 in Figure 2 . At concentrations above 40% sucrose a decrease of k is observed; this point is indicated with arrow 2. The rotational correlation time for both spin probes after rewarming of a rapidly cooled 20% sucrose-water mixture is shown in Figure 3. Between -70 and -31 OC log rc decreases almost linearly with temperature. At temperatures between -31 and -28 OC (as indicated with arrows in Figure 3), r, starts to decrease much stronger.
Discussion The mobility of spin probes, as expressed in rC,reflects the interaction between the probe and the solvent. This interaction, which contains solvation effects as well, is expressed in terms of the parameters k and S (eqs 1 and 2). This approach differs from a study carried out by Le Meste and Voilley.ls These authors expressed the change of the boundary layer conditions between the spin probes and the solvent from stickiness (complete interaction) to slip (no interaction) in terms of a change of the effective hydrodynamic radius of the probe. This approach, however, leads to molecular sizes much smaller than the actual size of the probes. In our approach, we start with the known sizes and shapes of the spin probes and express all solvation and interaction effects in the
Roozen and Hemminga parameters k and S. The parameter S is especially interesting since it is insensitive to molecular shape, thereby enabling comparison between probes of different molecular shape. In the following discussion, it will be shown that in the mixtures considered here, the parameter S is a measure of hydrogen bonding between the probe and the solvent molecules. Hydrophobic interactions may be considered to be negligible.21 The formation of hydrogen bonds will be visualized as an acid-base reaction. Glycerol-Water Mixtures. As shown in Figure 1, S decreases for both probes as the glycerol content of a glycerol-water mixture increases up to 95%. This result agrees very well with results of Le Meste and V0i1ley.I~ The decrease of S implies that both probes will interact stronger with water than with glycerol molecules. Therefore, at increasing glycerol contents the slip will increase. This is in agreement with the statements of D O U Z O U . ~ ~ Douzou stated that glycerol is sufficiently more basic in character than water to behave as a hydrogen acceptor, rather than as an amphoteric compound. Spin probe I is a secondary alcohol, so that it slightly prefers to accept a hydrogen bond rather than to offer it.34 Spin probe I1 is a diketone and is a stronger base than spin probe I. The decrease of S with glycerol content in aqueous glycerol mixtures is therefore in agreement with the acid-base aspects of the formation of a hydrogen bond. As can be seen in Figure 1, probe I hardly interacts with anhydrous glycerol. Probe 11, however, interacts strongly with the same solvent. This probe will, due to its relatively strong basic character, form a solvation shell with the amphoteric glycerol molecules. If a small amount of water is added to anhydrous glycerol, the glycerol molecules in the solvation shell of probe I1 will be replaced by the smaller water molecules. This leads to a decrease of its hydrodynamic volume and explains the minimum of parameter S at low water contents. The glycerol content of the mixture at which a minimum in S can be observed depends on the ratio of the spin probe concentration to the water concentration and, as described above, on the size of the solvation shell. (For practical reasons it has not been possible to vary the spin probe concentration in the region of low water content in a systematic way.) Similar effects have been observed in translation diffusion of different solutes in methanol-water mixture^.^' Also in this case, the minimum in the hydrodynamic volume is explained by replacement of methanol molecules in the solvation shell of the solutes by the smaller water molecules. The observed differences between the values for parameter S of the two probes at low glycerol contents are relatively small. Since S is independent of the molecular shape of the probes, this can be due to a different dynamic behavior of the probes (i.e., anisotropic and internal motion) as well as to uncertainties in the values selected for V and 8. Sucrose- Water Mixtures. In Figure 2 , it can be seen that the value of parameter k in sucrose-water mixtures between 0 and 40 wt % (=3.4 mol/mol %) is constant and close to I . This is explained by the fact that the probe molecules can form many hydrogen bonds with the liquid. Due to the relative basic character of the probes, they will form hydrogen bonds with water rather than with sucrose molecules. It is known from other studies that the hydrogen bonds between the sucrose and water molecules in an aqueous sucrose solution are stronger or more extensive than the bonds between water molecules t h e m ~ e l v e s . ~ ~ ~ ~ ~ At concentrations above 40% sucrose a decrease of parameter k is observed (arrow 2 in Figure 2 ) . This is explained by the fact that fewer hydrogen bonds are formed between the spin probes and the solvent. This is in agreement with the conclusions of Flinklo that sucrose-water mixtures at concentrations over 30-40% sucrose change from a solution of hydrated sucrose molecules to a sucrose-water phase, in which all the water molecules directly or indirectly (Le., as a second layer) are involved in hydrogen bonds ~~ from translation with sucrose. Also, S ~ h l i e p h a k econcluded (34) Douzou, P. Cryobiochemisfry: An Introduction; Academic Press: Orlando, FL, 1977. (35) Longsworth, L. G. J . Phys. Chem. 1963, 67, 659. (36) Taylor, J. B.; Rowlinson, J. S. Trans. Faraday Sac. 1955, 51, 1183. (37) Sugett. A . J . Solution Chem. 1976, 5. 33.
Molecular Motion in Sucrose Mixtures diffusion experiments that above 40% sucrose a sucrose association ~ ~Mathlouthi et structure is formed. Mathlouthi and L U Uand aI.,@ using laser Raman spectroscopy, found that at 35% sucrose the hydrogen-bond network changes. Richardson et aI!l reached the same conclusions based on deuterium and oxygen-17 nuclear magnetic resonance measurements. All these findings fit within the interpretation of our ESR results. Arrow 1 in Figure 2 shows that parameter k equals 0 (and thus S becomes negative) at about 70 wt % sucrose (=11 mol/mol 76). A negative value of S is indicative of the formation of cavities. Cavities can be formed if the probes are not part of the lattice. It is possible that the cavities are not a property of the lattice but are induced by the probes itself. Dickenson and S y m o n con~~~ cluded from ESR experiments that CIOz molecules in water could be present in cavities. Many other authors have observed the presence of cavities in p0lymers.4"~ Jeffrey and LewisMdeduced from quantum mechanical calculations that sucrose molecules in concentrated sucrose-water mixtures tend to orient themselves in such a way that the hydroxyl groups form chains, because it is more favorable for OH groups to be both a hydrogen-bond donor and an acceptor. The anomeric hydroxyl groups, because of their weak acceptor property, will tend to function as 'chain stoppers". This will result in almost equal populations of finite and infinite chains.46 Thus, it is reasonable to assume that a concentrated sucrose solution can have a polymer-like character in which cavities can be formed. Sucrose- Water Mixtures at Subzero Temperatures. According to experimental observations in our laboratory (data not shown) at temperatures where a part of the water is frozen, the spin probes are not present in the ice lattice but in the concentrated amorphous solution (which is called CAS in the following discussion). This is in agreement with results of other studies!' In Figure 3 it can be observed that the mobility of the spin probes starts to increase strongly between -33 and -28 OC. This is explained by the glass transition of the mixture, which is at -32 OC, as has been determined by several author^.^^^^ Due to this transition the Stokes (38) Schliephake, D. Zucker 1965, 18, 138. (39) Mathlouthi, M.; Luu, C. Carbohydr. Res. 1980, 81, 203. (40) Mathlouthi, M.; Luu, C.; Meffroy-Bigget, A. M.; Luu, D. V . Carbohydr. Res. 1980,8/, 213. (41) Richardson, S.J.; Baianu, I. C.; Steinberg, M . P. J . Food Sci. 1987, 52, 806.
(42) Dickenson, L. C.; Symons, M. C. R. Trans. Faraday SOC.1969,66, 1334. (43) Brandt, W . W. J . Phys. Chem. 1959, 63, 1080. (44) Menting. L. C. Retention of volatiles during the air drying of aqueous carbohydrate solutions. Ph.D. Thesis, Eindhoven, 1970. (45) TormPIa, P. Eur. Polym. J . 1973, 10, 519. (46) Jeffrey, G. A.; Lewis, L. Carbohydr. Res. 1978, 60, 179. (47) Yoshioka, H . Chem. Left. 1977, 1153.
The Journal of Physical Chemistry, Vol. 94, No. 18, 1990 1329
viscosity of the CAS decreases by the following effects6 (1) According to the concept of "unfrozen water" defined by Franks,% melting of ice starts at the glass transition temperature, giving rise to a plastizing on the CAS. (2) When the temperature rises to reach the glass transition temperature, the 'free volume of the mixture" (this is the volume of the mixture which is not "occupied" by molecules) starts to increase. This free volume now permits molecules to diffuse and results a dramatic decrease of the Stokes viscosity O C C U ~ S . ~ ~ * ~ ~ The reduction of 7 for a 20% sucrose-water by these effects is from about 10l2Paes at the glass transition temperature to about IO3 Pams at temperatures 20 OC above the glass transitions6 The relative decrease of T ~ as, shown in Figure 3, is, however, much smaller. It should be noted that a 20% sucrose-water mixture at temperatures below the glass transition consits of ice and a glassy sucrose-water mixture. When the ice starts to melt due to the glass transition (the first effect mentioned above), the parameter k will increase strongly as can be seen from Figure 2. This effect will reduce the decrease of T~ due to the glass transition. At -50 OC the rotational correlation time is about lo-" s (Figure 3), so that k is about (given a viscosity of 1 O l 2 Pa-s"). This very low value of k implies that the spin probes are present in cavities in the lattice of the amorphous solution, not being part of the lattice. Spin probe I1 is somewhat more mobile in the glassy sucrosesystem than probe I. Possibly, the distortion of the lattice due to the presence of probe I is smaller than that due to the presence of the less spherical probe 11. From our experiments it can be concluded that the changes in macroscopic observable properties of the mixture, as determined by differential scanning calorimetric measurements, agree very well with the results obtained by means of rotational diffusion measurements of spin probe molecules. In the present paper we have demonstrated that ESR is a powerful technique to obtain information about hydrogen bonds, mobility, and formation of cavities in a sucrose-water system and may be a suitable technique to obtain information about the hydration of several other sugars. Similar effects as described here have been carried out on (ma1to)dextrin-water mixtures. The results will be published elsewhere. Acknowledgment. We are grateful to Unilever Research, Colworth House, UK, for financial support. We thank P. Walstra and T. van Vliet for many stimulating discussions. (48) McKenzie, A. P. Philos. Trans. R. SOC.London 1977, 278, 167. (49) Levine, H.; Slade, L. Cryo-Lett. 1988, 9, 21. (50) Franks, F. Cryo-Lett. 1986, 7 , 207. (51) Williams, M. L.; Landel, R. F.; Ferry, D. J. J . Am. Chem. Soc. 1955, 77, 3701. (52) Soesanto, T.; Williams, M . C. J . Phys. Chem. 1981, 85, 3338.
